Rock Strength Research Articles

Dynamic mechanical properties of sandstone with two circular inclusions under impact loading

Inclusions are often present in rock defects, which can compensate for some of the problems of low rock strength and poor stability caused by hole defects. Specimens containing inclusions exhibit different mechanical properties under dynamic loading, and the strength change, energy evolution law and fracture mechanism deserve to be clearly discussed. In this work, a dynamic impact test of sandstone with circular inclusions was carried out. The failure process of each sample was recorded by a high-speed camera, and the influences of the inclusion strength and strain rate on the dynamic impact performance of the sandstone were analysed. Increasing the strain rate and inclusion strength can significantly improve the dynamic compressive strength of a sample. The dissipated energy density and impact toughness index are positively correlated with the strain rate. The dissipated energy density increased the most when the sample type was FA, at 10.6%. When the sample type was FD, the impact toughness index increased the most, which was 49.1%. In the early stage of loading, the localized strain is mainly concentrated inside the filler and gradually evolves into deformation of the filler and extension of shear cracks in the late stage of loading. The failure modes of a sample are not the result of a single factor but are influenced by both the strain rate and the filler. The types of cracks in the samples are mainly shear cracks and shear–tension composite cracks.

Prediction of Rock Unloading Strength Based on PSO-XGBoost Hybrid Models.

Rock excavation is essentially an unloading behavior, and its mechanical properties are significantly different from those under loading conditions. In response to the current deficiencies in the peak strength prediction of rocks under unloading conditions, this study proposes a hybrid learning model for the intelligent prediction of the unloading strength of rocks using simple parameters in rock unloading tests. The XGBoost technique was used to construct a model, and the PSO-XGBoost hybrid model was developed by employing particle swarm optimization (PSO) to refine the XGBoost parameters for better prediction. In order to verify the validity and accuracy of the proposed hybrid model, 134 rock sample sets containing various common rock types in rock excavation were collected from international and Chinese publications for the purpose of modeling, and the rock unloading strength prediction results were compared with those obtained by the Random Forest (RF) model, the Support Vector Machine (SVM) model, the XGBoost (XGBoost) model, and the Grid Search Method-based XGBoost (GS-XGBoost) model. Meanwhile, five statistical indicators, including the coefficient of determination (R2), mean absolute error (MAE), mean absolute percentage error (MAPE), mean square error (MSE), and root mean square error (RMSE), were calculated to check the acceptability of these models from a quantitative perspective. A review of the comparison results revealed that the proposed PSO-XGBoost hybrid model provides a better performance than the others in predicting rock unloading strength. Finally, the importance of the effect of each input feature on the generalization performance of the hybrid model was assessed. The insights garnered from this research offer a substantial reference for tunnel excavation design and other representative projects.

Dynamic optimization design of open-pit mine full-boundary slope considering uncertainty of rock mass strength

Rock and soil strength profoundly influences the stability of open-pit mine slopes. Traditional slope design, based on limited drilling data, often disregards inherent uncertainties. Effectively utilizing new sample information from mining operations poses a challenge, hindering dynamic and differentiated design for the entire perimeter slope. To address this, we propose a dynamic optimization method considering rock mass strength uncertainty for the entire perimeter slope. Our approach involves designing slope angles separately in different zones, while thoroughly considering decision-makers' preferences. Furthermore, we delegate the final adjustment authority of slope angles within the safety permissible range to on-site decision-makers. Compared to traditional methods, our dynamic design method incorporates rock mass strength uncertainty into slope evaluation while also accounting for decision-makers' safety and economic preferences. Through a case study of a specific open-pit mine, our proposed dynamic design method increases the overall slope angle by approximately 2.5°, fully accommodating the influence of on-site decision-making preferences on slope design. This article introduces a new method of dynamic optimization of open-pit mine slope based on simplified observation method, which improves the flexibility of decision-making and realizes the differential design of the whole surrounding slope.

Directional fracture patterns of excavated jointed rock mass within rough discrete fractures

The influence of the fractures on the anisotropic mechanical behavior of excavated fractured rock mass is important for the stability of rock tunnels. Rough joints were generated using fractal principles, and the Monte Carlo method was employed to create joint network faces. Biaxial compression numerical simulations were conducted using the discrete element method to analyze the behavior of the rock mass containing these networks. Quantitative analysis was carried out to evaluate the strength variability and total number of cracks in the jointed rock mass. A linear regression analysis was conducted to establish the relationship between rock strength and excavation size. The findings demonstrate significant disparities between the linear and fractal models regarding rock damage mode, stress–strain curves, and crack evolution patterns. Tensile rupture and local shear damage were found to be the primary fracture modes for the fractured rock tunnels, forming a V-shaped damage zone within the central tunnel. The shape of this zone was influenced by fracture direction and excavation ratio. Excavation at the center of the rock mass substantially impacted the variability of rock strength and the occurrence of internal cracks. An increase in the slope ratio led to a greater variability of rock mass strength, transitioning from nearly isotropic to weakly anisotropic behavior. The total number of cracks exhibited a W-shaped trend, initially increasing and later decreasing as the slope ratio decreased. Additionally, a clear linear correlation was observed between rock strength and excavation ratio at the center of the rock mass.

Fatigue damage evolution behaviors and fractional fatigue mechanical model of monzogabbro under true triaxial disturbance test

The disturbance wave caused by excavation or blasting of underground surrounding rock causes fatigue degradation effect of rock and eventually leads to disasters. However, the fatigue damage characteristics and fatigue models of rock under true triaxial disturbance are scare. Therefore, a series of true triaxial disturbance tests were conducted to investigate the rock fatigue deformation, strength and damage behaviors under different conditions. The evolutions of static damage and fatigue damage are separated and investigated respectively. Fatigue deformation and damage of rock under true triaxial stress undergoes three stages: attenuation, constant velocity and acceleration stage. The crack initiation stress can be as the initial condition of the fatigue deformation; the fatigue critical stress σdc of rock entering the acceleration failure stage was proposed and explored, with increasing frequency, σdc increase slightly and with increasing σ2, σdc increase obviously. Then, a novel fractional fatigue mechanical model considering the fatigue damage and intermediate principal stress effects of rock under true triaxial disturbance was proposed. The theoretical results of the model agree well with the results of the tests. Finally, the sensitivity analysis of stresses and model parameters and the model predictions under other untesting conditions were carried out to improve the understanding and prediction level of fatigue failure in underground engineering.

Uniaxial compressive strength prediction based on measurement while drilling data: A laboratory study

The uniaxial compressive strength is one of the most important basic parameters of rock, which is essential for surrounding rock stability analysis and support scheme design of underground engineering. At present, it is time consuming and costly to take a large amount of core samples for laboratory testing, and the mechanical properties of the cores may be affected by mining disturbance, which can easily lead to inaccurate result. The measurement while drilling (MWD) technology provides a new approach to solve the above challenge. The key to implementing this technology is to establish a correlation model between drilling parameters and rock mechanics parameters. Based on the characteristics of polycrystalline diamond compact (PDC) bits in drilling and rock breakage, this paper analyzes the mechanical state of the bit in breaking rock. A theoretical correlation model between the torque, feed force of the bit and the uniaxial compressive strength of the rock has been developed. To verify the accuracy of the theoretical model, the uniaxial compressive strength of five different types of rocks (red sandstone, green sandstone, limestone, marble and shale) was obtained through laboratory mechanical tests. The torque Mb, feed force Fb and other parameters in the drilling process of these five rocks were tested through the newly developed MWD test system. The correlation between the drilling parameters and the uniaxial compressive strength of rock was established. The results showed that the feed force Fb and torque Mb measured at five different types of rocks indicate a linear increasing trend with an increase in depth of cut h. Meanwhile, a strong linear relationship between the feed force Fb and torque Mb is evident. This paper proposes an MWD-based method to rapidly conduct the in-situ measurement of the uniaxial compressive strength of various rocks.

Experimental study on effect of cyclic gas pressure on mechanical and acoustic emission characteristics of salt rock

The utilization of renewable resources like wind and solar energy has led the Chinese government to prioritize the development of energy storage systems, garnering significant attention for salt cavern compressed air energy storage (CAES) technology. The stability of the surrounding rock in salt caverns is critical for ensuring sustained operation. By conducting mechanical tests on salt rock under fixed axial and confining pressures with cyclic gas pressure, the mechanical behavior and acoustic emission characteristics of salt rock under the influence of gas pressure were analyzed. The mechanical and acoustic emission characteristics of salt rock were analyzed. The results indicated that the triaxial compressive strength of salt rock negatively correlated with constant gas pressure. Both radial and axial strains demonstrated distinct phases: deceleration, steady-state, and acceleration. The steady-state creep rate of axial strain and the lower limit of cyclic gas pressure can be fitted in the form of an exponential function. The number of cyclic air pressure cycles decreased as the lower limit of cyclic air pressure increased. Acoustic emission count was used to define the damage variables, clarifying the formation and accumulation of salt rock damage in each stage, distinguishing the growth rates of damage during loading and unloading. It was observed that the higher the lower limit of cyclic air pressure, the quicker the damage accumulated with cycling. During the test, the absolute energy of the acoustic emissions from the salt rock conformed to a damped power-law distribution. The power-law distribution index γ of the absolute energy of acoustic emissions shifted with the number of cyclic air pressure cycles, and the sudden decrease of the distribution index γ plays a certain early warning role for the failure of salt rock.

Study on crack propagation mechanism and acoustic-thermal sensitivity analysis of pre-cracked weakly cemented rock

As the intensity and depth of coal mining gradually increase, environmental disturbances become more complex, and the degree of crack development in weakly cemented surrounding rocks continues to increase. In order to study the influence mechanism of crack angle on the fracture mechanism and acoustic − thermal precursor information of weakly cemented rocks, visual biaxial loading tests were conducted on pre-cracked weakly cemented rocks based on a transparent servo loading device, combined with digital speckle correlation method (DSCM), acoustic emission (AE), and infrared thermal imaging (ITI). The research results indicate that as the inclination angle of cracks increases, the initial strength, peak strength, and elastic modulus of rocks exhibit a logarithmic relationship of first decreasing and then increasing. When the inclination angle of the crack increases from < 30° to > 75°, the failure mode of weakly cemented rocks changes from shear to tension. The propagation path of deformation localization is consistent with the propagation trajectory of surface cracks, and the extension length and time of tensile cracks are longer than those of shear cracks. The acoustic − thermal sensitivity of weakly cemented rocks with crack inclination angle of > 45° is higher than that with crack inclination angle of ≤ 30°. The research results contribute to further understanding and mastering the mechanism of crack initiation and propagation in weakly cemented rocks containing joints, and provide theoretical guidance for engineering methods to control the deformation of weakly cemented surrounding rocks.

DNN–GA–RF prediction model for rock strength indicators based on sound level and drilling parameters

DNN–GA–RF prediction model for rock strength indicators based on sound level and drilling parameters

Stress-deformation analysis of the cracked elastic body

A new analytical plane Elastic Fracture Mechanics (LEFM) model of the effective elastic moduli exhibited by an isotropic elastic cracked solid in tensile and compressive stress fields is presented. The effective Young’s modulus and Poisson’s ratio E¯,v¯, respectively, relate the stresses applied to the cracked solid with its macroscopic deformation. In the case of a compressive stress field the effective elastic moduli depend solely on properly oriented cracks that are either open or closed. This model is then used for the stress and displacement estimations around a circular axisymmetric hole under internal pressure and external hydrostatic stress. The creation of the hole alters the stresses in its neighborhood, and induces a deterioration of the elastic moduli. In this manner, the effective elastic moduli depend on the radial distance from the hole’s boundary. The validation of the algorithm was done against Kirsch’s analytical solution of the axisymmetric hole problem for nearly zero density of cracks as well as for large values of the friction angle. The model predicts a lower tangential stress concentration at the wall of the hole compared to that predicted by the constant linear elasticity solution and a maximum stress concentration that is not necessarily located at the wall of the hole. This apparent enhancement of rock strength adjacent to the wall is more pronounced for larger concentrations of open cracks.

Experimental study of the end effect on the mechanical behaviors of rocks under true 3D compressions

AbstractIn true triaxial compression tests, all three principal stresses are imposed independently. This allows for a more comprehensive analysis of the material's mechanical properties. The end effect in true triaxial compression tests is a crucial phenomenon that impacts the accuracy and reliability of the test results. In this study, a series of true triaxial compression tests is conducted to examine the influence of the end friction on the mechanical properties. The laboratory results show that the presence of the end friction could bring about an apparent increase in rock strength and also restrict the deformation in each direction showing that the stiffness (the slope of the curves) increased slightly. The rock strength could be enhanced from 24.7 to 90.7 () when the end friction is increased, which is mainly caused by the lateral interface friction. The failure mode and fracture angle of the specimen are also influenced by the end effect, showing that under high friction conditions, the failure is more ductile, and a larger fracture angle is observed. At last, in comparison with the published experimental data, the actual specific friction angle (corresponding friction coefficient is about 0.19) for the direct specimen–metal contacts in a true 3D test is numerically identified, which is empirically reasonable and higher than the tested range 0.146–0.157 obtained from double‐shear test system.

Estimating Uniaxial Compressive Strength of Sedimentary Rocks with Leeb hardness Using SVM Regression Analysis and Artificial Neural Networks

Estimating Uniaxial Compressive Strength of Sedimentary Rocks with Leeb hardness Using SVM Regression Analysis and Artificial Neural Networks

Rate effect of rocks: Insights from DEM modeling

Rocks are subjected to different loading rates at different construction stages and engineering applications. The strength of rock usually increases with loading rate. This rate dependency is one of the time-dependent behaviors of rock, whereby the micro-mechanisms are believed to be the subcritical crack growth due to stress corrosions. However, no evidence is provided yet. This study investigated rate effects of rocks through a novel implementation of Parallel-Bonded Stress Corrosion (PSC) model in Discrete Element Method (DEM). Long-term microparameters in PSC are first calibrated through creep test. Then, a series of uniaxial compressive strength, direct tensile strength, and triaxial compressive strength tests are performed, with strain rates ranging from 1×10−7/s to 1×10−3/s. Results show that the uniaxial compressive strength is highly dependent on strain rates which quantitatively matches with the experimental data. At lower strain rate, more subcritical cracks propagate due to longer stress-corrosion reaction time, resulting in a lower strength. Besides, strain rate also influences the failure patterns in post-peak, with single failure plane at lower strain rates and multiple failure planes at higher strain rates. Rate effects are also observed in direct tensile strength tests, with similar rate of increase in strength and a transition in cracking pattern, which align with the experimental data, indicating tension-induced subcritical cracking is the unified underlying micro-mechanism of rate effects for both cases. However, in triaxial compressive strength tests, rate effects become less obvious with increasing confining pressure, consistent with experimental findings, as subcritical crack growth is suppressed in shearing processes.

Assessment of the influence of roughness, concrete adhesion and scale effect on the shear strength of concrete-gneiss rock interfaces

Assessment of the influence of roughness, concrete adhesion and scale effect on the shear strength of concrete-gneiss rock interfaces

Quantifying uncertainty in rock mass properties: Implications for GSI, RMi, and RMR assessments

Probability-based empirical methods were employed as an alternative approach to predicting uncertainties associated with rock mass properties. The focus was on developing probabilistic spreadsheets to forecast rock mass classification indexes. Histograms were constructed to describe the best distribution in predicting rock mass properties. The developed models also offer utility in predicting the impact of discontinuities within the rock mass on rock strength and rock mass classification systems. Statistical analyses identified volumetric joint count, joint spacing, joint frequency, and rock strength as the most influential parameters. Moreover, the statistical analysis revealed varying degrees of correlation among different rock mass properties. While some properties demonstrated significant correlations suitable for modelling, others did not align well with any correlation model. The results highlight the need for a comprehensive approach to rock mass characterization, considering multiple factors beyond volumetric joint count. Geological complexities, including tectonic activity and weathering processes, may obscure direct correlations. These results emphasize the importance of empirical modelling and detailed site investigations for accurate assessment of rock mass quality and stability in the Himalaya.

Leeb Hardness Approach in the Determination of Strength after Accelerated Weathering Tests

ABSTRACT This study aimed to investigate the usability of the Leeb hardness test in determining changes in strength as a result of atmospheric weathering in works of cultural heritage built with low-strength pyroclastic rocks. To this end, the effects of weathering processes on strength properties were investigated in two building stones commonly used in Niğde province located in the Cappadocia (Turkey) region, which contains the most important works of cultural heritage created using low-strength pyroclastic rocks. The index, strength, mineralogical, and petrographic properties of rocks were first investigated. Then, freeze–thaw (F-T) and salt crystallization (SC) tests, the weathering processes of which consisted of six periods, were performed on samples prepared in cubic form. After the F-T and SC processes, the macro change in the samples and changes in weight loss, uniaxial compressive strength (UCS), and Leeb hardness (HL) values were determined. Highly correlated linear relationships were obtained between the SC and F-T cycles of the samples and the UCS and HL values. The HL test was applied to samples for which the UCS test could not be applied due to the loss of sample integrity after the advancing cycles of the accelerated weathering tests. Linear relationships with high correlation were determined between the UCS and HL values obtained from the samples after the accelerated weathering test. This study revealed that the HL approach could be used as an alternative in modeling the strength parameters of the weathering processes of the structures of cultural heritage built using low-strength rocks.

Probabilistic evaluation method for the stability of large underground cavern considering the uncertainty of rock mass mechanical parameters: A case study of Baihetan underground powerhouse project

For deep large underground cavern projects under complex geological conditions, the determination of rock mass mechanical parameters and stability analysis is fraught with a great deal of uncertainty. This paper proposes a set of methods for estimating rock mass mechanical parameters and probabilistic stability assessment suitable for construction characteristics of large underground caverns. On the one hand, according to the Hoek-Brown criterion and Monte Carlo simulation, a dynamic estimation method for rock mass mechanical parameters is proposed by using Rock Mass Rating (RMR), the uniaxial compressive strength (UCS) of intact rock, and the material constant (mb) as input parameters. On the other hand, considering the uncertainty of rock mass mechanical parameters, a probabilistic evaluation method applicable to the unloading response characteristics of rock mass (including displacement and fracturing zones) around the large cavern is put forward, combining the point estimation method and numerical simulation. The proposed methods were applied to an underground powerhouse, with an excavation span of 34 m and height of 88.7 m, at the Baihetan hydropower station in the southwest of China. Based on extensive field investigations and tests, the probability distributions of key rock mass mechanical parameters were obtained. Furthermore, the high sensitivity of input parameters in the H-B criterion for estimating rock mass mechanical parameters were revealed. Through dynamic simulation, the probability distributions of the displacement and fracturing zones in surrounding rock during the layer-by-layer excavation of the cavern were presented. Comprehensive on-site tests showed that the simulated results were in basic agreement with the actual unloading response behavior during the cavern excavation, validating the correctness and applicability of the proposed methods. The study provides a relatively comprehensive approach for estimating rock mass mechanical parameters and stability evaluation in similar underground engineering projects, and also has guiding significance for predicting and preventing engineering rock mass hazards.

Geochemical, Mineralogical, and Fluid Processes in the Brittle‐Plastic Transition of Continental Crust

AbstractThe brittle‐plastic transition (BPT), the strongest part of the crust, is critical to continental geodynamics but is poorly understood relative to simpler crust above and below. It is typically represented as a depth transition from brittle/frictional to plastic/viscous deformation controlled by temperature and pressure. Footwalls of low‐angle normal faults (LANFs) exhumed through the BPT provide rock records that challenge this view. Three well‐studied LANF footwalls are reviewed. All record geochemical, mineralogical and fluid‐related controls on embrittlement, not just monotonic P‐T decrease. Two quartz‐rich examples record embrittlement at unexpectedly high T (≥450–500°C) that was modulated by wetting characteristics of fluids. One had an inverted BPT: brittle fracture beneath contemporaneous mylonites. In another study, a brittle LANF grew from plastic mylonites due to mineralogic changes that strengthened parts, causing initial frictional slip and cataclasis on weak planes that ultimately linked. In all, geologically abrupt small‐scale processes controlled behavior at kilometer scales. Similar processes likely affect other tectonic settings and seismic cycles. Such processes offer fertile research opportunities in continental geodynamics; they will be increasingly tractable as computational abilities improve. Adaptive, multi‐scale approaches including the effects of fluid‐rock geochemistry and mineralogical changes on rock strength and deformation are needed. Thoughtful modeling approaches may yield key insights into the positive and negative feedbacks that are likely. Discontinuous deformation is probably needed explicitly along with exploration of initial and boundary conditions.

Study on crack propagation characteristics of rocks with different lateral pressure based on joint monitoring of DIC and AE

During the process of rock failure, the characteristics of crack propagation affect the fracture characteristics and macroscopic mechanical behavior of rocks, indirectly affecting the safety and stability of rock engineering. In order to study the evolution characteristics of cracks during rock failure under different lateral pressure, based on an improved digital image correlation (DIC) and acoustic emission (AE) signal recognition method, a visual biaxial servo loading device was developed to conduct biaxial compression tests on mudstone with prefabricated cracks of the same inclination angle. The research results indicate that the stages of crack propagation include microcracks propagation, crack tip formation, stable macroscopic cracks propagation, and unstable macroscopic cracks propagation. As the lateral pressure increased, the initiation frequency of cracks decreased, the quantity of propagation decreased, and the propagation path shortened, indirectly increasing the bearing strength of rocks. The initiation stress, peak stress, and elastic modulus of pre-cracked rocks with lateral pressure ≤ 2 MPa were lower than those of pre-cracked rocks with lateral pressure > 3 MPa, with the minimum reduction amplitude of 14.1%, 21.2%, and 12.6%, respectively. As the lateral pressure decreased, the dispersion of the AE main frequency distribution increased and accelerated its downward expansion. The surface temperature curves of rocks were prone to fluctuations and rapid upward evolution characteristics corresponding to crack tip formation and crack propagation, respectively. The research results provide theoretical and engineering references for the mining of weak coal seams.

Estimating Time-to-Failure and Long-Term Strength of Rocks Based on Creep Strain Rate Model

Estimating Time-to-Failure and Long-Term Strength of Rocks Based on Creep Strain Rate Model